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C2 Logs
a) Given that y = log8 x, find expressions in terms of y for
i) log8 x^2,
ii) log2 x.
b) Hence, or otherwise, find the value of x such that
3 log8 x^2 + log2 x = 6.
Rep given
i) log8 x^2,
ii) log2 x.
b) Hence, or otherwise, find the value of x such that
3 log8 x^2 + log2 x = 6.
Rep given
Reply 1
Is it y=log8x or y=log8 * x
Reply 2
Assumming you mean log(base 8):
y = log(base 8) x
=> x = 8^y (*)
1. log(base 8) x^2 = 2.log(base 8) x [using basic log laws]
=> log(base 8) x^2 = 2y
2. From (*):
x = 8^y = (2^3)^y = 2^3y
Taking log(base 2) of each side:
log(base 2) x = 3y
3. Use these values in the equation given:
3.(2y) + 3y = 6
9y = 6
y = 1/3
Plug that back in (*) to get your value of x. Apologies if this is wrong, rushed through it
y = log(base 8) x
=> x = 8^y (*)
1. log(base 8) x^2 = 2.log(base 8) x [using basic log laws]
=> log(base 8) x^2 = 2y
2. From (*):
x = 8^y = (2^3)^y = 2^3y
Taking log(base 2) of each side:
log(base 2) x = 3y
3. Use these values in the equation given:
3.(2y) + 3y = 6
9y = 6
y = 1/3
Plug that back in (*) to get your value of x. Apologies if this is wrong, rushed through it
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